Finite Group Databasebeta

← #67×#625 #13172663

Subgroups — #67×#625 #13172663

Order 1728.

2100 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#67C212yesmaximal, complemented
2C22×C3×#625C211yesmaximal, characteristic, complemented
3C2×D3×#625C211yesmaximal, characteristic, complemented
4#11723717C211yesmaximal, characteristic, complemented
5#11723629C212yesmaximal, complemented
6#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#11723029C211yesmaximal, characteristic, complemented
8#11722956C212yesmaximal, complemented
9#11722953C211yesmaximal, characteristic, complemented
10#11722946C212yesmaximal, complemented
11Dic3×#625C211yesmaximal, characteristic, complemented
12#672—32nomaximal
13D4×#625—31nomaximal
14C23×C32×D3C2212yescomplemented
15C22×C3×D32C2212yescomplemented
16C2×C3×#638C2212yescomplemented
17C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
18C2×C32×#67C2211yescharacteristic
19C2×#6295C2211yescharacteristic, complemented
20C2×#6290C2212yescomplemented
21C2×#6290C2212yescomplemented
22C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
23C3×D3×#67—28no—
24C2×C3×#626C2212yescomplemented
25C2×C3×#625—24no—
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic, complemented
28C2×C3×#625C2212yescomplemented
29C2×C3×#625C2212yescomplemented
30C2×C3×D3×Dic3C2212yescomplemented
31D3×#625—24no—
32#88864C2211yescharacteristic, complemented
33#88815C2211yescharacteristic, complemented
34#88814C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39Dic3×C3⋊Dic3C2211yescharacteristic, complemented
40C22×C3×#67—32no—
41C22×C3×#67—32no—
42C2×C3×D3×D4—32no—
43C2×D3×#67—32no—
44C2×D3×#67D312yescomplemented
45C22×#625—31no—
46C22×#625D311yescharacteristic, complemented
47#64162—32no—
48D4×C3⋊Dic3—31no—
49#63983—32no—
50#63980—31no—
51#63980—31no—
52#63979—32no—
53#63978—32no—
54#63978—32no—
55#63976—32no—
56#63976—32no—
57#63976—32no—
58#63976—32no—
59#63976—62no—
60Dic3×#67—32no—
61Dic3×#67—32no—
62Dic3×#67—61no—
63#63970—32no—
64#63970—32no—
65#63914—31no—
66#63908—32no—
67C4×#625—31no—
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3C2312yes—
70C22×C32×D3—24no—
71C22×C32×D3—24no—
72C22×C32×D3—42no—
73C22×C32×D3C2312yes—
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2312yes—
76C2×C3×D32—24no—
77C2×C3×D32—24no—
78C2×C3×D32—42no—
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
81C3×#638—24no—
82C2×C3×C3⋊Dic3—22no—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C32×#67D414yescomplemented
87C2×C32×Dic3C2311yescharacteristic
88#6295—22no—
89#6290—24no—
90#6290—42no—
91D3×C3⋊Dic3—22no—
92C3×#626—24no—
93C3×#625—24no—
94C3×#625—24no—
95C3×#625—22no—
96C3×#625D414yescomplemented
97C3×D3×Dic3—24no—
98D4×#67—92no—
99D4×#67—91no—
100C24×C32—32no—
101C23×C3×D3—22no—
102C23×C3×D3—32no—
103C23×C3×D3—32no—
104C23×C3×D3C2×D312yescomplemented
105C23×C3×D3C2×D312yescomplemented
106C22×D32C2×D312yescomplemented
107C2×C32×D4—31no—
108C2×#638—32no—
109C2×#638—32no—
110C2×#638C2×D312yescomplemented
111C22×C3⋊Dic3—31no—
112C22×C3⋊Dic3C2×D311yescharacteristic, complemented
113C2×C3×#67—21no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—32no—
121C2×C3×#67—32no—
122C2×C3×#67—32no—
123C2×C3×#67—68no—
124C2×C3×#67—68no—
125C2×C3×#67—62no—
126C2×C3×#67C2×D312yes—
127C22×C3×Dic3—32no—
128C22×C3×Dic3—32no—
129C22×C3×Dic3—61no—
130C3×D3×D4—68no—
131C2×C3×D12—32no—
132C2×C3×C4×D3—32no—
133D3×#67—28no—
134D3×#67—68no—
135C2×#626—32no—
136C2×#626C2×D312yescomplemented
137C2×#625—24no—
138C2×#625—32no—
139C2×#625—32no—
140C2×#625—31no—
141C2×#625—32no—
142C2×#625—32no—
143C2×#625—64no—
144C2×#625—62no—
145C2×#625—62no—
146C2×#625C2×D311yescharacteristic
147C2×#625C2×D312yescomplemented
148C2×#625C2×D311yescharacteristic, complemented
149C2×#625C2×D312yescomplemented
150C2×D3×Dic3—32no—
151C2×D3×Dic3—61no—
152C2×D3×Dic3C2×D312yescomplemented
153#3757—31no—
154#3757—32no—
155#3757—31no—
156#3757—32no—
157#3757—32no—
158#3757—61no—
159#3757—62no—
160#3757—121no—
161C4⋊(C3⋊Dic3)—31no—
162C4×C3⋊Dic3—31no—
163#3724—31no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—61no—
167#3722—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—61no—
176(C2×D3)⋊Dic3—62no—
177(C2×D3)⋊Dic3—62no—
178Dic32—32no—
179Dic32—61no—
180C22×C33—21no—
181C22×C33—21no—
182C22×C33C2×D412yescomplemented
183C22×C33C2411yescharacteristic
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3—22no—
187C2×C32×D3—22no—
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3—22no—
191C2×C32×D3—22no—
192C2×C32×D3—22no—
193C2×C32×D3—22no—
194C2×C32×D3—48no—
195C2×C32×D3C2×D414yescomplemented
196C2×C32×D3C2×D412yescomplemented
197C3×D32—48no—
198C3⋊(C3⋊Dic3)—21no—
199C3⋊(C3⋊Dic3)—21no—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3C2×D412yescomplemented
203C32×Dic3C2×D412yescomplemented
204C22×C3×D4—92no—
205C22×C3×D4—91no—
206C22×#67—32no—
207C22×#67—32no—
208C22×#67—92no—
209C2×D3×D4—32no—
210C2×D3×D4—91no—
211#953—92no—
212#953—92no—
213#953—92no—
214#953—182no—
215#940—92no—
216#940—91no—
217#939—92no—
218#939—92no—
219#939—92no—
220#938—92no—
221#938—91no—
222#937—92no—
223#937—92no—
224#937—92no—
225D4×Dic3—91no—
226D4×Dic3—92no—
227D4×Dic3—181no—
228#930—92no—
229#930—91no—
230C4×#67—92no—
231C4×#67—91no—
232C23×C32—22no—
233C23×C32—21no—
234C23×C32—31no—
235C23×C32—32no—
236C23×C32—32no—
237C23×C32—41no—
238C23×C32—64no—
239C23×C32—64no—
240C23×C32—122no—
241C23×C32C22×D311yescharacteristic
242C23×C32C22×D312yes—
243C22×C3⋊D3C22×D312yes—
244C22×C3×D3—24no—
245C22×C3×D3—24no—
246C22×C3×D3—24no—
247C22×C3×D3—24no—
248C22×C3×D3—22no—
249C22×C3×D3—22no—
250C22×C3×D3—21no—
251C22×C3×D3—32no—
252C22×C3×D3—32no—
253C22×C3×D3—44no—
254C22×C3×D3—44no—
255C22×C3×D3—42no—
256C22×C3×D3—42no—
257C22×C3×D3—44no—
258C22×C3×D3—62no—
259C22×C3×D3—64no—
260C22×C3×D3—64no—
261C22×C3×D3—64no—
262C22×C3×D3—64no—
263C22×C3×D3—122no—
264C22×C3×D3—122no—
265C22×C3×D3C22×D312yes—
266C22×C3×D3C22×D312yes—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C22×D312yes—
269C22×C3×D3C22×D312yes—
270C2×D32—24no—
271C2×D32—24no—
272C2×D32—42no—
273C32×D4—34no—
274C2×C32×C4—31no—
275#638—24no—
276#638—64no—
277#638—122no—
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3—32no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—32no—
283C2×C3⋊Dic3—61no—
284C2×C3⋊Dic3—62no—
285C2×C3⋊Dic3—62no—
286C2×C3⋊Dic3—61no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—121no—
289C2×C3⋊Dic3—121no—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D312yes—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C3×#67—24no—
294C3×#67—38no—
295C3×#67—64no—
296C3×#67—64no—
297C3×#67—64no—
298C3×#67—64no—
299C3×#67—64no—
300C3×#67—64no—
301C3×#67—64no—
302C3×#67—64no—
303C3×#67—124no—
304C3×#67#6718yescomplemented
305C2×C3×Dic3—21no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—62no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—64no—
314C2×C3×Dic3—64no—
315C2×C3×Dic3—122no—
316C2×C3×Dic3C22×D312yes—
317C3×D12—64no—
318C3×C4×D3—64no—
319#626—24no—
320#626—64no—
321#625—24no—
322#625—24no—
323#625—22no—
324#625—64no—
325#625—64no—
326#625—62no—
327#625—124no—
328#625—122no—
329#625—122no—
330#625—124no—
331#625#6714yesdirect product factor
332D3×Dic3—24no—
333D3×Dic3—64no—
334D3×Dic3—122no—
335D42—271noSylow
336C2×C33—22no—
337C2×C33C22×D411yescharacteristic
338C2×C33C22×D411yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C3×C3⋊D3—42no—
341C32×D3—22no—
342C32×D3—24no—
343C32×D3—42no—
344C24×C3—32no—
345C24×C3—32no—
346C24×C3—62no—
347C24×C3—92no—
348C23×D3—32no—
349C23×D3—32no—
350C23×D3D3212yescomplemented
351C2×C3×D4—32no—
352C2×C3×D4—61no—
353C2×C3×D4—92no—
354C2×C3×D4—91no—
355C2×C3×D4—92no—
356C2×C3×D4—92no—
357C2×C3×D4—91no—
358C2×C3×D4—92no—
359C2×C3×D4—188no—
360C2×C3×D4—184no—
361C22×C3×C4—92no—
362C22×C3×C4—91no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—32no—
366C2×#67—32no—
367C2×#67—32no—
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—32no—
371C2×#67—32no—
372C2×#67—62no—
373C2×#67—68no—
374C2×#67—68no—
375C2×#67—92no—
376C2×#67—92no—
377C2×#67—92no—
378C2×#67—92no—
379C2×#67—92no—
380C2×#67—92no—
381C2×#67—92no—
382C2×#67—182no—
383C2×#67—182no—
384C2×#67—188no—
385C2×#67D3211yescharacteristic
386C22×Dic3—32no—
387C22×Dic3—32no—
388C22×Dic3—61no—
389C22×Dic3—92no—
390C22×Dic3—181no—
391D3×D4—68no—
392D3×D4—184no—
393C2×D12—32no—
394C2×D12—91no—
395C2×C4×D3—32no—
396C2×C4×D3—91no—
397#217—92no—
398#217—92no—
399#217—92no—
400#217—92no—
401#217—92no—
402#217—92no—
403#217—91no—
404#217—92no—
405#217—181no—
406#217—182no—
407#217—182no—
408#217—181no—
409#217—182no—
410#217—361no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—92no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—92no—
416C4⋊Dic3—91no—
417C4⋊Dic3—92no—
418C4⋊Dic3—181no—
419Dic3⋊C4—92no—
420Dic3⋊C4—91no—
421C4×Dic3—92no—
422C4×Dic3—91no—
423C4×Dic3—181no—
424C22×C32—22no—
425C22×C32—21no—
426C22×C32—22no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—24no—
432C22×C32—34no—
433C22×C32—32no—
434C22×C32—41no—
435C22×C32—42no—
436C22×C32—41no—
437C22×C32—42no—
438C22×C32—42no—
439C22×C32—41no—
440C22×C32—62no—
441C22×C32—61no—
442C22×C32—62no—
443C22×C32—62no—
444C22×C32—61no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32—81no—
448C22×C32—81no—
449C22×C32—128no—
450C22×C32D3×D412yescomplemented
451C22×C32C2×#6714yescomplemented
452C22×C32C23×D312yes—
453C22×C32C23×D311yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—24no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—24no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—42no—
475C2×C3×D3—42no—
476C2×C3×D3—42no—
477C2×C3×D3—42no—
478C2×C3×D3—48no—
479C2×C3×D3—48no—
480C2×C3×D3—416no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—62no—
486C2×C3×D3—62no—
487C2×C3×D3—122no—
488C2×C3×D3—122no—
489C2×C3×D3—122no—
490C2×C3×D3—128no—
491C2×C3×D3—128no—
492C2×C3×D3D3×D414yescomplemented
493C2×C3×D3C2×#6714yescomplemented
494C2×C3×D3C2×#6714yescomplemented
495D32—48no—
496C32×C4—32no—
497C3⋊Dic3—22no—
498C3⋊Dic3—21no—
499C3⋊Dic3—62no—
500C3⋊Dic3—61no—
501C3⋊Dic3—62no—
502C3⋊Dic3—61no—
503C3⋊Dic3—121no—
504C3⋊Dic3—122no—
505C3⋊Dic3—122no—
506C3⋊Dic3—121no—
507C3⋊Dic3—241no—
508C3⋊Dic3—241no—
509C3⋊Dic3C2×#6712yescomplemented
510C3×Dic3—22no—
511C3×Dic3—34no—
512C3×Dic3—62no—
513C3×Dic3—62no—
514C3×Dic3—62no—
515C3×Dic3—62no—
516C3×Dic3—121no—
517C3×Dic3—122no—
518C3×Dic3C2×#6714yescomplemented
519C22×D4—92no—
520C22×D4—91no—
521C22×D4—271no—
522#127—271no—
523#121—272no—
524#121—271no—
525#121—271no—
526#120—272no—
527#120—272no—
528C4×D4—271no—
529C4×D4—271no—
530C33D4211yescharacteristic, complemented, Sylow
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—32no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—41no—
539C23×C3—61no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—64no—
543C23×C3—64no—
544C23×C3—64no—
545C23×C3—64no—
546C23×C3—92no—
547C23×C3—124no—
548C23×C3—124no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—124no—
552C23×C3—184no—
553C23×C3—184no—
554C23×C3—362no—
555C23×C3C2×D3211yescharacteristic
556C23×C3C2×D3212yes—
557C22×D3—24no—
558C22×D3—24no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—42no—
562C22×D3—62no—
563C22×D3—64no—
564C22×D3—64no—
565C22×D3—64no—
566C22×D3—64no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3C2×D3212yes—
570C22×D3C2×D3211yescharacteristic
571C22×D3C2×D3212yes—
572C3×D4—38no—
573C3×D4—64no—
574C3×D4—94no—
575C3×D4—184no—
576C3×D4—182no—
577C3×D4—184no—
578C3×D4—184no—
579C3×D4—184no—
580C2×C3×C4—32no—
581C2×C3×C4—61no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—92no—
585C2×C3×C4—184no—
586C2×C3×C4—182no—
587#67—38no—
588#67—64no—
589#67—64no—
590#67—64no—
591#67—64no—
592#67—64no—
593#67—64no—
594#67—64no—
595#67—64no—
596#67—124no—
597#67—184no—
598#67—184no—
599#67—184no—
600#67—184no—
601#67—364no—
602#67—362no—
603#67—362no—
604#67—362no—
605#67—364no—
606#67#62514yesdirect product factor
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—64no—
615C2×Dic3—64no—
616C2×Dic3—91no—
617C2×Dic3—92no—
618C2×Dic3—91no—
619C2×Dic3—92no—
620C2×Dic3—122no—
621C2×Dic3—181no—
622C2×Dic3—181no—
623C2×Dic3—182no—
624C2×Dic3—182no—
625C2×Dic3—184no—
626C2×Dic3—361no—
627C2×Dic3—361no—
628C2×Dic3—362no—
629C2×Dic3C2×D3211yescharacteristic
630D12—64no—
631D12—182no—
632C4×D3—64no—
633C4×D3—182no—
634C2×C32—22no—
635C2×C32—24no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—22no—
640C2×C32—22no—
641C2×C32—22no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—44no—
646C2×C32—42no—
647C2×C32—62no—
648C2×C32—64no—
649C2×C32—82no—
650C2×C32—122no—
651C2×C32C2×D3×D412yes—
652C2×C32C2×D3×D411yescharacteristic
653C2×C32#100412yes—
654C2×C32#100411yescharacteristic
655C2×C32C22×#6712yes—
656C2×C32C22×#6711yescharacteristic
657C3⋊D3—42no—
658C3×D3—24no—
659C3×D3—24no—
660C3×D3—24no—
661C3×D3—42no—
662C3×D3—44no—
663C3×D3—44no—
664C3×D3—42no—
665C3×D3—42no—
666C3×D3—122no—
667C3×D3—122no—
668C3×D3—242no—
669C24—32no—
670C24—92no—
671C2×D4—31no—
672C2×D4—92no—
673C2×D4—91no—
674C2×D4—92no—
675C2×D4—92no—
676C2×D4—91no—
677C2×D4—92no—
678C2×D4—188no—
679C2×D4—184no—
680C2×D4—271no—
681C2×D4—272no—
682C2×D4—272no—
683C2×D4—544no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—271no—
687C4⋊C4—271no—
688C4⋊C4—271no—
689C22⋊C4—272no—
690C22⋊C4—272no—
691C22⋊C4—271no—
692C22⋊C4—272no—
693C22⋊C4—271no—
694C42—271no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—24no—
702C22×C3—22no—
703C22×C3—34no—
704C22×C3—34no—
705C22×C3—34no—
706C22×C3—41no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—42no—
712C22×C3—64no—
713C22×C3—62no—
714C22×C3—64no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—122no—
734C22×C3—121no—
735C22×C3—128no—
736C22×C3—128no—
737C22×C3—1216no—
738C22×C3—182no—
739C22×C3—182no—
740C22×C3—182no—
741C22×C3—368no—
742C22×C3C2×#62512yescomplemented
743C22×C3D3×#6714yescomplemented
744C22×C3C22×D3211yescharacteristic
745C22×C3C22×D3212yes—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—48no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—128no—
764C2×D3—128no—
765C2×D3C2×#62512yescomplemented
766C2×D3D3×#6714yescomplemented
767C3×C4—34no—
768C3×C4—62no—
769C3×C4—92no—
770C3×C4—181no—
771C3×C4—182no—
772Dic3—34no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—121no—
778Dic3—122no—
779Dic3—181no—
780Dic3—181no—
781Dic3—182no—
782Dic3—182no—
783Dic3—361no—
784Dic3—362no—
785Dic3—362no—
786Dic3—361no—
787Dic3—721no—
788Dic3—721no—
789Dic3C2×#62512yescomplemented
790C32—21no—
791C32—22no—
792C32—41no—
793C32D4×#6712yescomplemented
794C32D4×#6711yescharacteristic, complemented
795C23—32no—
796C23—31no—
797C23—32no—
798C23—64no—
799C23—64no—
800C23—92no—
801C23—122no—
802C23—184no—
803C23—184no—
804C23—362no—
805C23D3311yescharacteristic
806D4—34no—
807D4—94no—
808D4—184no—
809D4—182no—
810D4—184no—
811D4—184no—
812D4—184no—
813D4—542no—
814D4—544no—
815D4—1082no—
816C2×C4—31no—
817C2×C4—91no—
818C2×C4—92no—
819C2×C4—91no—
820C2×C4—184no—
821C2×C4—182no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C3—22no—
826C2×C3—24no—
827C2×C3—22no—
828C2×C3—21no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—22no—
833C2×C3—44no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—64no—
839C2×C3—64no—
840C2×C3—64no—
841C2×C3—82no—
842C2×C3—124no—
843C2×C3—122no—
844C2×C3—124no—
845C2×C3—122no—
846C2×C3—122no—
847C2×C3—362no—
848C2×C3D32×D411yescharacteristic
849C2×C3#6431311yescharacteristic
850C2×C3C22×#62511yescharacteristic
851C2×C3C2×D3×#6712yes—
852C2×C3C2×D3×#6712yes—
853C2×C3#6433012yes—
854D3—22no—
855D3—24no—
856D3—42no—
857D3—122no—
858D3—122no—
859D3—242no—
860C22—21no—
861C22—21no—
862C22—32no—
863C22—34no—
864C22—62no—
865C22—62no—
866C22—61no—
867C22—61no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—128no—
872C22—182no—
873C22—182no—
874C22—182no—
875C22—368no—
876C22D3×#62512yescomplemented
877C22C2×D3311yescharacteristic
878C4—32no—
879C4—92no—
880C4—182no—
881C4—181no—
882C4—541no—
883C4—541no—
884C3—22no—
885C3—21no—
886C3—41no—
887C3D4×#62511yescharacteristic, complemented
888C3#67212yescomplemented
889C2—22no—
890C2—64no—
891C2—62no—
892C2—122no—
893C2—362no—
894C2C2×D3×#62511yescharacteristic
895C2#1172441411yescharacteristic
896C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×D3×#67C2semidirect
2. C22×C3×#625C2semidirect
3. C2×D3×#625C2semidirect
4. #11723717C2semidirect
5. #11723629C2semidirect
6. #67×C3⋊Dic3C2semidirect
7. #11723029C2semidirect
8. #11722956C2semidirect
9. #11722953C2semidirect
10. #11722946C2semidirect
11. Dic3×#625C2semidirect
14. C23×C32×D3C22semidirect
15. C22×C3×D32C22semidirect
16. C2×C3×#638C22semidirect
17. C22×C3×C3⋊Dic3C22semidirect
19. C2×#6295C22semidirect
20. C2×#6290C22semidirect
21. C2×#6290C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#626C22semidirect
27. C2×C3×#625C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×#625C22semidirect
30. C2×C3×D3×Dic3C22semidirect
32. #88864C22semidirect
33. #88815C22semidirect
34. #88814C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
39. Dic3×C3⋊Dic3C22semidirect
44. C2×D3×#67D3semidirect
46. C22×#625D3semidirect
86. C32×#67D4semidirect
96. C3×#625D4semidirect
104. C23×C3×D3C2×D3semidirect
105. C23×C3×D3C2×D3semidirect
106. C22×D32C2×D3semidirect
110. C2×#638C2×D3semidirect
112. C22×C3⋊Dic3C2×D3semidirect
136. C2×#626C2×D3semidirect
147. C2×#625C2×D3semidirect
148. C2×#625C2×D3semidirect
149. C2×#625C2×D3semidirect
152. C2×D3×Dic3C2×D3semidirect
182. C22×C33C2×D4semidirect
195. C2×C32×D3C2×D4semidirect
196. C2×C32×D3C2×D4semidirect
202. C3×C3⋊Dic3C2×D4semidirect
203. C32×Dic3C2×D4semidirect
304. C3×#67#67semidirect
331. #625#67direct (N × H)
350. C23×D3D32semidirect
450. C22×C32D3×D4semidirect
451. C22×C32C2×#67semidirect
492. C2×C3×D3D3×D4semidirect
493. C2×C3×D3C2×#67semidirect
494. C2×C3×D3C2×#67semidirect
509. C3⋊Dic3C2×#67semidirect
518. C3×Dic3C2×#67semidirect
530. C33D42semidirect
606. #67#625direct (N × H)
742. C22×C3C2×#625semidirect
743. C22×C3D3×#67semidirect
765. C2×D3C2×#625semidirect
766. C2×D3D3×#67semidirect
789. Dic3C2×#625semidirect
793. C32D4×#67semidirect
794. C32D4×#67semidirect
876. C22D3×#625semidirect
887. C3D4×#625semidirect
888. C3#672semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×D3×#672
C22×C3×#6252
C2×D3×#6252
#117237172
#117236292
#67×C3⋊Dic32
#117230292
#117229562
#117229532
#117229462
Dic3×#6252
#6723
D4×#6253